AS 2 Maths Topic 3 Statistical Sampling

Census
1. Advantages
2. Disadvantages

Observes or measure every member of a population
1. It should give a completely accurate result
2. -Time consuming and expensive
- Cannot be used when the testing process destroys the item
- Difficult to process a large quantity

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Sample
1. Advantages
2. Disadvantages

A selection of observations taken from a subset of the population which is used to find out info about the population as a whole
1. - Less time consuming and more cost effective that census.
- Fewer people have to respond
- Less data to process than in a

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Sample
Disadvantages

Data may not be as accurate
Sample may not be large enough to give info. about the small subset of the population

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How to carry out simple random sampling
5 steps

1. A sampling frame, usually a list.
2. Each person or thing allocated a unique number
3. Two methods of choosing numbers, generating random numbers and lottery sampling
4. Select the people as per random number generated
5. Ignore any repeats

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Lottery Sampling

Numbers of the sampling frame could be written on a tickets and placed into a 'hat'. The required number of tickets would then be drawn

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Systematic Sampling

The required elements are chosen at regular intervals from an ordered list
The first person to be chosen should be chosen at random

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Stratified Sampling

Population is divided mutually exclusive strata and a random sample is taken from each

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Equation for Stratified Sampling

No. of people in stratum = (no. in stratum/ no. in population ) x overall sample size

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Simple random sampling
Advantages
Disadvantages

1. Free of bias
2. Easy and cheap for small samples & populations
3. Each sampling unit has a known and equal chance of selection

1. Not suitable when the population size is large
2. Sampling frame needed

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Systematic sampling

1. Simple and quick to use
2. Suitable for large populations & samples

1. A sampling frame is needed
2. Can introduce bias if sampling frame is not random

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Stratified Sampling

1. Sample accurately reflects population structure
2. Guarantees proportional representation of groups within population

1. Population must be clearly classified into distinct strata
2. Selection from within each strata suffers from same disadvantage as

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Non-random sampling
Two types

Quota Sampling
Opportunity Sampling

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Quota Sampling

An interviewer or researcher selects a sample that reflects the characteristics of the whole population

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Quota Sampling
Advantages
Disadvantages

1. Allows a small sample to be representative
2. No sampling frame required
3. Quick , easy and inexpensive
4. Allows for easy comparison between different groups

1. Non-random sampling can introduce bias
2. Population must be divided into groups which c

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Opportunity/ convenience sampling

Consists of taking the sample from people who are available at the time the study is carried out and who fit the criteria you are looking for
e.g. first 20 people you meet outside a supermarket on a Monday

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Opportunity/ convenience sampling
Advantages
Disadvantages

1. Easy to carry out
2. Inexpensive

1. Unlikely to provide a representative sample
2. Highly dependent on individual research

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Discrete Data and examples

A variable is said to be discrete of it can only take particular values e.g. shoe size, cost of an item, no. of cars in a car park.

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Continuous data and examples

A variable is said to be continuous if it can take any values within a given range e.g. height, time, volume, weight

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Common mistake

Class BOUNDARIES are only if data us continuous. If this is the case we go 0.5 above and below the limits (in the table) to get the class boundaries

Class width - difference between BOUNDARIES
Midpoint - halfway between LIMITS

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Common mistake

Data can be continuous if its wrote like a-b or a<x>b. However wrote a-b, boundaries are half above and below
If wrote a<x>b, boundaries are a and b

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How to use calculator to generate random numbers

Press alpha "RanInt" and select a range using shift comma to separate number

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AS 2 Maths Topic 3 Statistical Sampling

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